Positron transmission experiments were performed on free-standing poly(methylmethacrylate) (PMMA) and polystyrene (PS) films of nanometric thicknesses made by spin coating. The power_law equation z(1/2)(E))=(alpha/rho)E-n was determined from the measurements of the S-parameter as a function of the positron implantation energy. These transmission experiments indicate that n = 1.90(+/-0.08) and alpha = 1.33(+/-0.10) mu g cm(-2) which deviates from the values found by Algers et al. (n = 1.71(+/-0.05) and alpha = 2.8(+/-0.2) mu g cm(-2)) and the commonly used parameters (n = 1.6 and alpha = 4.0 mu g cm(-2)).